Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T05:41:04.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Reformulating the Cube Law for Proportional Representation Elections

Published online by Cambridge University Press:  01 August 2014

Rein Taagepera
Rein Taagepera*
Affiliation:
University of California, Irvine
Get access Rights & Permissions [Opens in a new window]

Abstract

The cube law was proposed around 1910 to express the conversion of a party's vote shares into its seat share in two-party plurality elections with single-seat districts. This article develops predictive seat-vote equations for a much wider range of elections, including those involving many parties, single- and multi-seat districts, and diverse seat allocation rules such as plurality and list proportional representation (PR). Without any statistical curve fitting based on the seat and vote shares themselves, the basic features of the conversion are predicted using exogenous parameters: magnitude and number of districts, number of parties, and total size of the electorate and of the assembly. The link between the proposed equations and the original cube law is explicated. Using an existing data base, the fit of the predictive model is examined. On balance, this model accounts well for the conversion of votes to seats, and for the deviation from proportionality in PR systems.

Type
Articles
Information
American Political Science Review , Volume 80 , Issue 2 , June 1986 , pp. 489 - 504
Copyright
Copyright © American Political Science Association 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Coleman, James S. 1964. Introduction to Mathematical Sociology. New York: Free Press of Glencoe.Google Scholar
Cox, Edward F. 1972. State and National Voting: 1910–1970. Hamden, CT: Archon Books.Google Scholar
Grofman, Bernard. 1975. A Review of Macro-Election Systems. In Wildenmann, Rudolf, ed., Sozialwissenschaftliches Jahrbuch für Politik, vol. 4. Munich: Günter Olzog Verlag, pp. 303–52.Google Scholar
Grofman, Bernard. 1983. Measures of Bias and Proportionality in Seats-Votes Relationships. Political Methodology, 9:295–327.Google Scholar
Gudgin, Graham, and Taylor, Peter. 1979. Seats, Votes, and the Spatial Organisation of Elections. London: Pion Limited.Google Scholar
Kendall, M. G., and Stuart, A.. 1950. The Law of Cubic Proportion in Election Results. British Journal of Sociology, 1:183–97.Google Scholar
Laakso, Markku. 1979. Should a Two-and-a-Half Law Replace the Cube Law in British Elections? British Journal of Political Science, 9:355–84.Google Scholar
Laakso, Markku, and Taagepera, Rein. 1979. Effective Number of Parties: A Measure with Application to West Europe. Comparative Political Studies, 12:3–27.Google Scholar
Lijphart, Arend. 1984a. Advances in the Comparative Study of Electoral Systems. World Politics, 36:424–36.Google Scholar
Lijphart, Arend. 1984b. Democracies: Patterns of Majoritarian and Consensus Government in Twenty-One Countries. New Haven and London: Yale University Press.Google Scholar
March, James G. 1957. Party Legislative Representation as a Function of Election Results. Public Opinion Quarterly, 21:521–24.Google Scholar
Nohlen, Dieter. 1978. Wahlsysteme der Welt [Electoral Systems of the World]. München: Piper.Google Scholar
Qualter, Terence H. 1968. Seats and Votes: An Application of the Cube Law to the Canadian Electoral System. Canadian Journal of Political Science, 1:336–44.Google Scholar
Quandt, Richard E. 1974. A Stochastic Model of Elections in Two-Party Systems. Journal of the American Statistical Association, 69:315–24.Google Scholar
Rae, Douglas W. 1971. The Political Consequences of Electoral Laws. New Haven, CT: Yale University Press.Google Scholar
Sankoff, David, and Mellos, Koula. 1972. The Swing Ratio and Game Theory. American Political Science Review, 66:551–54.CrossRefGoogle Scholar
Sartori, Giovanni. 1968. Representational Systems. International Encyclopedia of the Social Sciences, vol. 13. New York: Macmillan & Free Press.Google Scholar
Schrodt, Philip A. 1981. A Statistical Study of the Cube Law in Five Electoral Systems. Political Methodology, 7:31–54.Google Scholar
Taagepera, Rein. 1972. The Size of National Assemblies. Social Science Research, 1:385–401.Google Scholar
Taagepera, Rein. 1973. Seats and Votes: A Generalization of the Cube Law of Elections. Social Science Research, 2:257–75.Google Scholar
Taagepera, Rein. 1984. Effect of District Magnitude and Properties of Two-Seat Districts. In Lijphart, Arend and Grofman, Bernard, eds., Choosing an Electoral System: Issues and Alternatives. New York: Praeger, 91–101.Google Scholar
Taagepera, Rein, and Laakso, Markku. 1980. Proportionality Profiles of West European Electoral Systems. European Journal of Political Research, 8:423–46.CrossRefGoogle Scholar
Theil, Henri. 1969. The Desired Political Entropy. American Political Science Review, 63:521–25.Google Scholar
Theil, Henri. 1970. The Cube Law Revisited. Journal of American Statistical Association, 65:1213–19.Google Scholar
Tufte, Edward R. 1973. The Relationship Between Seats and Votes in Two-Party Systems. American Political Science Review, 67:540–47.Google Scholar
Vick, Alan J. 1979. Proportionality Profiles of the United States Congress: 1910–1970. Unpublished manuscript.Google Scholar
Submit a response

Comments

No Comments have been published for this article.